phew, played around a bit more and I've managed to get to:

  $_ = $response->content;
  m/GENERAL SYNOPSIS AT ([0-9]{4})<BR>\n((^.+<BR>\n)+)<P>/mi;
  print "===> ".$1."  ".$2."\n";
[download]

which gives me the output of

===> 0100  LOW SOUTH FITZROY 1000 MOVING SLOWLY NORTH AND FILLING 1006 BY 0100<BR>
TOMORROW. NEW LOW EXPECTED 50 MILES WEST OF TRAFALGAR 1007 BY SAME<BR>
TIME. HIGH 100 MILES WEST OF ROCKALL 1023 SLOW MOVING AND DECLINING<BR>
1021 BY THAT TIME<BR>

which is what I wanted.

But is that the best regex to get that result?